The students have worked on a lesson where they pretended to be Grandma's Famous Cookie Production Company. While they worked on that lesson very well, I realized they needed more specific work discriminating between the two types of division. Critical Area #1 in 3rd grade is "Developing understanding of multiplication and division and strategies for multiplication and division within 100." In the description of this understanding, the following points are made:

Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations.

For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size.

Therefore, I decided to spend another day or two having them "act out" situations and recording the outcomes.

If you try this lesson, I suggest you do it for at least two days so the concepts become habit for the students before they begin reading word problems.

Why More of the Same?

Real World Applications: Why More of the Same?

Division by Sharing Vs. Grouping (Day 2)

Division by Sharing Vs. Grouping (Day 2)

Unit 4: Understanding Division
Lesson 6 of 13

Objective: Students will be able to share objects equally to find quotients, or use known quotients to find missing factors.

When the students arrive at the community area, I ask them to form a circle. I then ask a student to be my partner to help me act out some stories about cookie orders for our Production Company (yesterday's lesson). This modeling strategy is called Fishbowl and works well when you are using manipulatives.

I have cubes and cups to represent our cookies and packages. I have a chart on the board already with 3 columns: Total, Cookies Per Package, Number of Packages. I ordered the columns in this way to model a division equation, but I am not using the symbol yet.

If you use this mini lesson, tell different stories to the students and ask them to help you fill in the chart with your known information and then act out what needs to be done to find the missing factor or the missing quotient. Possible stories may be:

We have 27 cookies baked. We can put 3 cookies into each package. How many packages can we fill?

We have 27 cookies baked. We have 7 packages to fill. How many cookies can we put in each?

When you are ready to send the students off to work on their own, you may want to consider having them work with partners. The conversations and teamwork is always helpful in concept development. It also helps me assess understanding when I can eavesdrop!

When I have the students move into the active phase of the lesson, I hand them baggies with cubes and cups. I also fill in different parts of our chart on the board and ask them to copy it into their math journals. These will be the situations they work to solve. I usually have all work done in the journals, instead of a worksheet, as it acts as a glossary for the students as we go through the year.

As the students work, I typically stand by and listen in. Many times I ask them to explain what they are doing, why they are doing it, or prompt them to dig deeper. This is a perfect time to do some one-on-one or small group work as well.

These boys did not have a strategy when they began. I prompt them to consider the chart more and talk with me about what "per" means. Then the lightbulb lit!

This group is also working on a grouping task and were not in agreement of the outcome.

In this clip, the student explains that they "passed out" the cubes in to the nine packages.

To close each of these two sessions, I have students come up and share how they solve the problems on our chart. As each partnership completes explaining, I ask if anyone did it differently. This is a great time to stretch your students' thinking. You never know what the responses will be here, but the debates and different ways of thinking are always valuable. Don't skip this part.

Patricia, I am very pleased that this lesson was helpful for you. My students enjoyed it as well:) I think that student explanation, either verbally or written, is crucial to their growth as real learners in a community. If I can ever help with strategies to build "talk", let me know. Enjoy your summer.

I really liked the strategies you used to show students different ways to divide. They are simple and easy for students to do, at the same time they are understanding the concept of division. Your lesson plans are clear and show exactly what to do, thanks. I like how your students can explain their thinking process using the lesson content vocabulary. I can replicate the lesson with my students, thanks.

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Big Idea:
Just like multiplication, addition, and subtraction, division problems involve patterns and there are methodical ways in which manipulatives can be used to solve division problems with small dividends and divisors of 1 through 10.